title: SIMULATING BIOCHEMICAL SIGNALING NETWORKS IN COMPLEX MOVING GEOMETRIES.
abstract: Signaling networks regulate cellular responses to environmental stimuli through cascades of protein interactions. External signals can trigger cells to polarize and move in a specific direction. During migration, spatially localized activity of proteins is maintained. To investigate the effects of morphological changes on intracellular signaling, we developed a numerical scheme consisting of a cut cell finite volume spatial discretization coupled with level set methods to simulate the resulting advection-reaction-diffusion system. We then apply the method to several biochemical reaction networks in changing geometries. We found that a Turing instability can develop exclusively by cell deformations that maintain constant area. For a Turing system with a geometry-dependent single or double peak solution, simulations in a dynamically changing geometry suggest that a single peak solution is the only stable one, independent of the oscillation frequency. The method is also applied to a model of a signaling network in a migrating fibroblast.
authors.affiliation: Carolina Center for Interdisciplinary Applied Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599.
authors.forename: Wanda
authors.initials: W
authors.lastname: Strychalski
authors.forename: David
authors.initials: D
authors.lastname: Adalsteinsson
authors.forename: Timothy C
authors.initials: TC
authors.lastname: Elston
keywords: Advection-reaction-diffusion equation; Level set methods; Numerical methods; Systems biology